Combinatorial group theory

Combinatorial group theory is the study of patterns and structures involving groups, which are sets of objects that can be added, multiplied, or otherwise moved around together. For example, if you had two groups of four balls, each group has four balls in it. With combinatorial group theory, you can look at the patterns that can be created when the groups are combined. For example, you could look at how the balls could be arranged in a circle when the two groups of four balls are combined. You could also look at how different groups of different sizes can fit together in certain ways. Combinatorial group theory is used to study many different things, such as chemistry, physics, and even math.